5. A beach ball of mass 500grams falls from a height of 4m and hits the ground with a speed of 5m/sec. a). What is the work done on the ball by air resistance? b). What is the average force of the air resistance?

The potential energy of the ball before it falls is (mass) (gravity) (height) =

(0.5 kg) (9.8 m/s²) (4 m) = 19.6 joules

The kinetic energy of the ball when it hits the ground is (1/2) (mass) (speed) ² =

(1/2) (0.5 kg) (5 m/s) ² = (0.25 kg) (25 m²/s²) = 6.25 joules

a). The energy lost to air resistance during the fall is (19.6J - 6.25J) = 13.35 Joules. Energy is never destroyed, so these missing joules had to go somewhere. This is the work done on the ball by air resistance during the fall of the ball.

b). Air resistance worked on the ball all during the fall of 4 meters.

Work = (force) x (distance)

13.35 Joules = (force) x (4 meters)

Divide each side by (4 meters):

Average force = (13.35 Joules / 4 meters)

Average force = 3.3375 Newtons